Due 3/14/14 No Later Than 11:55PM PST

Introduction to Mineral Physics

Spring 2014

Midterm Exam

(Due 3/14/14 no later than 11:55PM PST)

This is an open book take home essay exam. Please do not discuss your answers with other people whether they be other students in the class or people at your home institution. However, feel free to improve your understanding of anything involved in answering the questions by any means available to you including reviewing the recorded lectures and other class materials, reading text books and journal articles and asking for additional clarification from faculty involved in the course or at your home institution.

For three of the following six questions provide a detailed answer – on the order of 200-400 words – that would be understandable to an undergraduate student. So you understand what I am expecting, I have provided you with sample question and answer [with commentary in square brackets].

[Question] Discuss the contents and uses of the International Tables for Crystallography Volume A.

[Answer]This document contains a complete description of the symmetry elements and a list of equivalent positions in a unit cell for each of the 230 space groups. Space groups are used to describe crystal structures therefore this volume is a very valuable reference for crystallographers. [This is a correct answer, but obviously it is too short. So now the answer continues with an explanation of the concepts that would be unfamiliar to an undergraduate]. You may recall from your mineralogy class [You don’t have to write your answer as if you were speaking to a student – this is just a comfortable way for me to structure my writing.] that symmetry elements are operations that allow one to repeat a motif (e.g. a group of atoms, a dot, a little picture etc.) in space. Point symmetry elements repeat the motif about a single point or plane (e.g. rotational axes, mirrors etc.). Translation symmetry elements repeat a motif through space and when they are combined in 3 dimensions they create lattices of repeating motifs. You may recall that there were 14 unique lattices called the Bravais lattices. There are also a few symmetry elements that combine translation and rotation or reflection, these are called screws and glides. Each space group is a unique combination of one of the 14 Bravais lattices and point symmetry elements and glides and or screws. The symmetry elements and the Bravais lattices can only be combined together in a limited number of ways – thus there are only 230 space groups as opposed to an extremely large number. A space group may contain quite a few symmetry operators, so it is not easy to visualize how, for example, the position of a single atom placed in the unit cell will be repeated by the all of the symmetry elements. To make life more convenient for crystallographers, this problem has been worked out for each space group and the equivalent positions for a motif occurring at an arbitrary position (x,y,z) are given along with the positions of the symmetry elements for each space group. [You may structure your answer any way that feels comfortable for you. You don’t need to use the structure that I have used; this is just an example. All I really want is for you go into enough detail and explain things clearly that I can see that you understand what you are writing about.]

Although it is not required, if you feel that your answer would be clearer if you included an illustration or two, feel free to do so. It is up to you to pick which three of the six questions you would like to answer.

Please submit your answers to 3 of these questions to me via e-mail () by the deadline given above.

1. Explain what an equation of state is and how equations of state are determined.

1. Discuss the methods that can be used to determine the pressure inside a sample in a multi-anvil experiment in the absence of a synchrotron.

1. Is single crystal or powder diffraction better for determining the atomic positions in a crystal structure? Explain you reasoning.

1. Explain the various ways in which heated DAC experiments can be conducted and what the pros and cons of each technique are.

1. You have been asked to conduct a phase equilibrium study in order to determine the position of the phase boundary between two polymorphs, over a pressure range from 5 to 10 GPa. The product and reactant are both solid phases and the reaction is reconstructive (a.k.a. civilian, or “nucleation and growth”) as opposed to displacive. Propose a credible experimental plan including what device you will use and how you will determine where the phase boundary is. Discuss any things you will need to watch out for and roughly how many experiments you will need to do to constrain the boundary.

1. Explain how high pressure experiments are useful for understanding the structure of the Earth’s interior. Illustrate your answer with at least one specific example.